Internal problem ID [14181]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }=-\cos \left (2 x \right )^{3} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 59
dsolve(tan(y(x))*sec(y(x))^2*diff(y(x),x)+cos(2*x)^3*sin(2*x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \operatorname {arccot}\left (\frac {8}{\sqrt {-2+4 \cos \left (4 x \right )^{2}-256 c_{1} +8 \cos \left (4 x \right )}}\right ) \\ y \left (x \right ) &= \frac {\pi }{2}+\arctan \left (\frac {8}{\sqrt {-2+4 \cos \left (4 x \right )^{2}-256 c_{1} +8 \cos \left (4 x \right )}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.982 (sec). Leaf size: 139
DSolve[Tan[y[x]]*Sec[y[x]]^2*y'[x]+Cos[2*x]^3*Sin[2*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\frac {\sqrt {8 \cos ^4(2 x)+c_1}}{4 \sqrt {2}}\right ) \\ y(x)\to \sec ^{-1}\left (-\frac {\sqrt {8 \cos ^4(2 x)+c_1}}{4 \sqrt {2}}\right ) \\ y(x)\to -\sec ^{-1}\left (\frac {\sqrt {8 \cos ^4(2 x)+c_1}}{4 \sqrt {2}}\right ) \\ y(x)\to \sec ^{-1}\left (\frac {\sqrt {8 \cos ^4(2 x)+c_1}}{4 \sqrt {2}}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}